I dont expect Kaido or Big Mom to do anything meaningful in this arc anymore. Once a main antagonist is defeated, they're just done as villains and we barely even see them. This will apply to Kaido as well. If we ever see him again it will be because he gives Luffy credit and talks about Joy boy and stuff like that. As we saw in that flashback when he spoke to King , he was waiting for Joy Boy to defeat him and thats what happened so he has fulfilled his role as antagonist.